{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7ef82b6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import emcee\n",
    "import DRW_library as dl\n",
    "import celerite\n",
    "from celerite import terms\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01f3dfef",
   "metadata": {},
   "outputs": [],
   "source": [
    "epochs=445\n",
    "tau=292"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a4489984",
   "metadata": {},
   "outputs": [],
   "source": [
    "def DRW_fit(t,s,err,mean):\n",
    "     # Define a cost function\n",
    "    def mle(params, y, gp):\n",
    "        gp.set_parameter_vector(params)\n",
    "        return -gp.log_likelihood(y)\n",
    "\n",
    "    def max_ap(params, y, gp):\n",
    "        gp.set_parameter_vector(params)\n",
    "        return -gp.log_likelihood(y)+0.5*params[0]-params[1]*0.5    \n",
    "\n",
    "    def log_probability(params):\n",
    "        gp.set_parameter_vector(params)\n",
    "        lp=gp.log_prior()\n",
    "        loga=gp.get_parameter_vector()[0]\n",
    "        logc=gp.get_parameter_vector()[1]\n",
    "        if not np.isfinite(lp):\n",
    "            return -np.inf\n",
    "        return gp.log_likelihood(s)+lp-0.5*loga+logc*0.5\n",
    "    \n",
    "    # Set up the GP model\n",
    "    bounds=dict(log_a=(2*np.log(0.02),2*np.log(0.7)),log_c=(-np.log(5000),0))\n",
    "    kernel=terms.RealTerm(log_a=np.log(0.1414),log_c=-np.log(400),bounds=bounds)\n",
    "    bounds=dict(log_sigma=(np.log(1e-300),np.log(0.3)))\n",
    "    kernel+=terms.JitterTerm(log_sigma=np.log(0.01),bounds=bounds)\n",
    "    gp=celerite.GP(kernel,mean=mean,fit_mean=True)\n",
    "    gp.compute(t,err)\n",
    "\n",
    "    initial_params = gp.get_parameter_vector()\n",
    "    soln = minimize(mle,initial_params,method=\"L-BFGS-B\",args=(s,gp))\n",
    "    gp.set_parameter_vector(soln.x)\n",
    "\n",
    "    rt=np.exp(-gp.get_parameter_vector()[1])\n",
    "    rs=np.exp(gp.get_parameter_vector()[0]/2)\n",
    "    re=np.exp(gp.get_parameter_vector()[2])\n",
    "    #MCMC\n",
    "    initial=np.array(soln.x)\n",
    "    ndim, nwalkers=len(initial),16\n",
    "    sampler=emcee.EnsembleSampler(nwalkers,ndim,log_probability)\n",
    "    #print(\"Running burn-in...\")\n",
    "    p0=initial+1e-4*np.random.randn(nwalkers,ndim)\n",
    "    p0,lp,_=sampler.run_mcmc(p0,125)\n",
    "    #print(\"Running production...\")\n",
    "    sampler.reset()\n",
    "    sampler.run_mcmc(p0,500)\n",
    "    \n",
    "    lt_chain=np.sort(-sampler.flatchain[:,1])\n",
    "    ls_chain=np.sort(sampler.flatchain[:,0]/2)\n",
    "    le_chain=np.sort(sampler.flatchain[:,2])\n",
    "    \n",
    "    t_e=np.mean(np.exp(lt_chain));s_e=np.mean(np.exp(ls_chain));e_e=np.mean(np.exp(le_chain))\n",
    "    t_m=np.exp(np.median(lt_chain));s_m=np.exp(np.median(ls_chain));e_m=np.exp(np.median(le_chain))\n",
    "\n",
    "\n",
    "    bounds=dict(log_a=(2*np.log(0.02),2*np.log(0.7)),log_c=(-np.log(5000),0))\n",
    "    kernel=terms.RealTerm(log_a=np.log(0.1414),log_c=-np.log(400),bounds=bounds)\n",
    "    bounds=dict(log_sigma=(np.log(1e-300),np.log(0.3)))\n",
    "    kernel+=terms.JitterTerm(log_sigma=np.log(0.01),bounds=bounds)\n",
    "    gp=celerite.GP(kernel,mean=mean,fit_mean=True)\n",
    "    gp.compute(t,err)\n",
    " \n",
    "    initial_params = gp.get_parameter_vector()\n",
    "    soln=minimize(max_ap,initial_params,method=\"L-BFGS-B\",args=(s,gp))\n",
    "    gp.set_parameter_vector(soln.x)\n",
    " \n",
    "    t_map=np.exp(-gp.get_parameter_vector()[1])\n",
    "    s_map=np.exp(gp.get_parameter_vector()[0]/2)\n",
    "    e_map=np.exp(gp.get_parameter_vector()[2])\n",
    "    print([rt,t_map,t_e,t_m],'\\n',[rs,s_map,s_e,s_m],'\\n',[re,e_map,e_e,e_m])\n",
    "    return sampler.flatchain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "09506c92",
   "metadata": {},
   "outputs": [],
   "source": [
    "def DRW_fit2(t,s,err,mean):\n",
    "     # Define a cost function\n",
    "    def mle(params, y, gp):\n",
    "        gp.set_parameter_vector(params)\n",
    "        return -gp.log_likelihood(y)\n",
    "\n",
    "    def max_ap(params, y, gp):\n",
    "        gp.set_parameter_vector(params)\n",
    "        return -gp.log_likelihood(y)+0.5*params[0]-params[1]*0.5    \n",
    "\n",
    "    def log_probability(params):\n",
    "        gp.set_parameter_vector(params)\n",
    "        lp=gp.log_prior()\n",
    "        loga=gp.get_parameter_dict().get('kernel:log_a')\n",
    "        logc=gp.get_parameter_dict().get('kernel:log_c')\n",
    "        if not np.isfinite(lp):\n",
    "            return -np.inf\n",
    "        return gp.log_likelihood(s)+lp-0.5*loga+logc*0.5\n",
    "    \n",
    "    # Set up the GP model\n",
    "    bounds=dict(log_a=(2*np.log(0.02),2*np.log(0.7)),log_c=(-np.log(5000),0))\n",
    "    kernel=terms.RealTerm(log_a=np.log(0.1414),log_c=-np.log(400),bounds=bounds)\n",
    "    gp=celerite.GP(kernel,mean=mean,fit_mean=True)\n",
    "    gp.compute(t,err)\n",
    "\n",
    "    initial_params = gp.get_parameter_vector()\n",
    "    soln = minimize(mle,initial_params,method=\"L-BFGS-B\",args=(s,gp))\n",
    "    gp.set_parameter_vector(soln.x)\n",
    "\n",
    "    rt=np.exp(-gp.get_parameter_dict().get('kernel:log_c'))\n",
    "    rs=np.exp(gp.get_parameter_dict().get('kernel:log_a')/2)\n",
    "    #MCMC\n",
    "    initial=np.array(soln.x)\n",
    "    ndim, nwalkers=len(initial),16\n",
    "    sampler=emcee.EnsembleSampler(nwalkers,ndim,log_probability)\n",
    "    #print(\"Running burn-in...\")\n",
    "    p0=initial+1e-4*np.random.randn(nwalkers,ndim)\n",
    "    p0,lp,_=sampler.run_mcmc(p0,125)\n",
    "    #print(\"Running production...\")\n",
    "    sampler.reset()\n",
    "    sampler.run_mcmc(p0,500)\n",
    "    \n",
    "    lt_chain=np.sort(-sampler.flatchain[:,1])\n",
    "    ls_chain=np.sort(sampler.flatchain[:,0]/2)\n",
    "    t_e=np.mean(np.exp(lt_chain));s_e=np.mean(np.exp(ls_chain))\n",
    "    t_m=np.exp(np.median(lt_chain));s_m=np.exp(np.median(ls_chain))\n",
    "\n",
    "    bounds=dict(log_a=(2*np.log(0.02),2*np.log(0.7)),log_c=(-np.log(5000),0))\n",
    "    kernel=terms.RealTerm(log_a=np.log(0.1414),log_c=-np.log(400),bounds=bounds)\n",
    "    gp=celerite.GP(kernel,mean=mean,fit_mean=True)\n",
    "    gp.compute(t,err)\n",
    " \n",
    "    initial_params = gp.get_parameter_vector()\n",
    "    soln=minimize(max_ap,initial_params,method=\"L-BFGS-B\",args=(s,gp))\n",
    "    gp.set_parameter_vector(soln.x)\n",
    " \n",
    "    t_map=np.exp(-gp.get_parameter_dict().get('kernel:log_c'))\n",
    "    s_map=np.exp(gp.get_parameter_dict().get('kernel:log_a')/2)\n",
    "    print([rt,t_map,t_e,t_m],'\\n',[rs,s_map,s_e,s_m])\n",
    "    return sampler.flatchain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "4facd8eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "t=np.sort(np.random.randint(0,2922,epochs)+\n",
    "          np.random.uniform(-0.13,0.13,epochs))\n",
    "y=dl.DRW_process(t,tau,0.2,18)\n",
    "\n",
    "ls_sdss=[]\n",
    "lsigma=[]\n",
    "for i in range(epochs):\n",
    "    #s=np.sqrt(0.004**2+np.exp(1.63*(y[i]-22.55)))\n",
    "    s=np.sqrt(0.013**2+np.exp(2*(y[i]-23.36)))\n",
    "    lsigma.append(s)\n",
    "    ls_sdss.append(np.random.normal(y[i],s,1)[0])\n",
    "s_sdss=np.array(ls_sdss)\n",
    "sigma=np.array(lsigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "2b83b181",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[249.29541416395986, 219.18520347284257, 496.899764025795, 335.89406249758594] \n",
      " [0.13006147034131557, 0.1222539369836286, 0.17010059530382562, 0.15096854126149611] \n",
      " [0.0024982001383267016, 0.0023752519161492403, 0.00015962575070056689, 1.465147571520591e-107]\n"
     ]
    }
   ],
   "source": [
    "chain=DRW_fit(t,s_sdss,sigma,np.mean(s_sdss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c32d55b9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[246.73940846887604, 217.3198921697951, 397.2843090137078, 276.10948893843204] \n",
      " [0.13013415398579964, 0.12236241787117641, 0.15417291451148557, 0.13760179681499798]\n"
     ]
    }
   ],
   "source": [
    "chain2=DRW_fit2(t,s_sdss,sigma,np.mean(s_sdss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "44403107",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1280x960 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=200)\n",
    "plt.plot(np.full(10,292),np.linspace(0,0.008,10),'k--',lw=5,alpha=0.3,label=r'$\\tau_{in}=292$ d')\n",
    "plt.hist(np.exp(-chain2[:,1]),bins=50,range=(0,1000),density=True,histtype='step',label='K17PMm')\n",
    "plt.hist(np.exp(-chain[:,1]),bins=50,range=(0,1000),density=True,histtype='step',alpha=0.7,\n",
    "         label=r'K17PMm($\\sigma_*$)')\n",
    "plt.xlabel(r'$\\tau_{\\rm out}/d$',fontsize=15)\n",
    "plt.ylabel(r'Probability',fontsize=15)\n",
    "plt.legend(fontsize=15)\n",
    "plt.ylim(0,0.005)\n",
    "plt.xlim(0,1000)\n",
    "plt.title(r'Marginalized posterior of $\\tau$($T=10\\tau_{\\rm in}$,N=445,$\\sigma_e=\\sigma_{\\rm OGLE}$)',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "0697bcd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1280x960 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=200)\n",
    "plt.plot(np.full(10,0.14),np.linspace(0,15,10),'k--',lw=5,alpha=0.3,label=r'$\\sigma_{in}=0.14$ mag')\n",
    "plt.hist(np.exp(chain2[:,0]/2),bins=50,range=(0,0.6),density=True,histtype='step',label='K17PMm')\n",
    "plt.hist(np.exp(chain[:,0]/2),bins=50,range=(0,0.6),density=True,histtype='step',alpha=0.7,\n",
    "         label=r'K17PMm($\\sigma_*$)')\n",
    "plt.xlabel(r'$\\sigma_{\\rm out}/mag$',fontsize=15)\n",
    "plt.ylabel(r'Probability',fontsize=15)\n",
    "plt.legend(fontsize=15)\n",
    "plt.title(r'Marginalized posterior of $\\sigma$($T=10\\tau_{\\rm in}$,N=445,$\\sigma_e=\\sigma_{\\rm OGLE}$)',fontsize=15)\n",
    "plt.ylim(0,15)\n",
    "plt.xlim(0,0.6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a009d64f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
